A Novel Statistical Independence Test for Dynamic Causal Discovery with Rare Events

Causal phenomena associated with rare events frequently occur across a wide range of engineering and mathematical problems, such as risk-sensitive safety analysis, accident analysis and prevention, and extreme value theory. However, current methods for causal discovery are often unable to uncover causal links between random variables that manifest only when the variables first experience low-probability realizations. To address this issue, we introduce a novel algorithm that performs statistical independence tests on data collected from time-invariant dynamical systems in which rare but consequential events occur. We seek to understand if the state of the dynamical system causally affects the likelihood of the rare event. In particular, we exploit the time-invariance of the underlying data to superimpose the occurrences of rare events, thus creating a new dataset, with rare events are better represented, on which conditional independence tests can be more efficiently performed. We provide non-asymptotic bounds for the consistency of our algorithm, and validate the performance of our algorithm across various simulated scenarios, with applications to traffic accidents.